Embodiments of the invention generally pertain to systems and methods for processing data. In particular, embodiments of the invention pertain to systems and methods for the soft detection and soft decoding of data.
Data transmitted in communication systems or data written in data storage systems is often subject to errors. Errors may occur for a number of reasons, including, for example, noise or interference in data transmission, defects in a data storage medium, and/or other reasons. Thus, the data received in such systems is inevitably a distorted version of the transmitted or written data. Some communication or data storage channels are subject to errors which are dependent on the data symbol being transmitted. For example, the statistics, such as the mean and variance, of the noise corrupting the signals corresponding to the data symbols are different for different symbols. Such channels are known as asymmetric channels.
One device that can be used to detect errors on an asymmetric channel is a channel detector. Channel detectors can act as a preprocessor of received data for error correcting devices known as decoders. Two types of channel detectors are hard detectors and soft detectors, and two types of decoders are hard decision decoders and soft decision decoders. Hard detectors can take a sequence of soft information from a channel and output hard decision data. The hard decision data includes data corresponding to the original encoded data symbols transmitted by the communications system. Hard decision decoders can then receive the hard decision data as input, and output decoded data symbols. On the other hand, a soft detector can take a sequence of soft information from a channel and outputs soft decision data. The soft decision data includes data that indicates the probability that the received encoded data are a particular data symbol, such as “0” or “1” in a binary system. Soft decision decoders can then take the soft decision data as input, and output decoded data symbols.
In soft detectors and soft decoders used in systems with binary channels, the ratio between the probability of a bit being “0” and the probability of a bit being “1” is used as a compact soft decision. This ratio is known as the likelihood ratio. Taking the logarithm of the likelihood ratio gives the log-likelihood ratio, or LLR. LLRs are one of the most commonly used representations of soft decisions in communication systems.
In practice, the accuracy of the LLRs produced by soft detectors often suffers when the communication or data storage channel is an asymmetric channel. As a result, the output of soft decision decoders can contain numerous errors. Thus, there is a continuing interest in enhancing the error detection capabilities of soft detectors and the error-correction capabilities of soft decision decoders on asymmetric channels.